AbstractLet σ(n) be the sum of the positive divisors of n, and let A(t) be the natural density of the set of positive integers n satisfying σ(n)/n⩾t. We give an improved asymptotic result for logA(t) as t grows unbounded. The same result holds if σ(n)/n is replaced by n/φ(n), where φ(n) is Eulerʼs totient function
In this work we will consider several questions concerning the asymptotic nature of arithmetic funct...
AbstractLet ps(n) = n−sζ(s) for n = 1,2,3,… and s > 1 be used to define a probability distribution P...
AbstractLet d(ω; α, γ) be the number of divisors of the Gaussian integer ω which lie in the arithmet...
AbstractLet σα(n) be the sum of the αth power of the positive divisors of n. We establish an asympto...
AbstractLet {ϵd} be a sequence of nonnegative numbers and f(n) = Σ ϵd, the sum being over divisors d...
Let σ(n)=∑d∣nd be the usual sum-of-divisors function. In 1933, Davenport showed that n/σ(n) possesse...
Plünnecke proved that if B ⊆ N is a basis of order h> 1, i.e., σ(hB) = 1, then σ(A+B)> σ(A)1 ...
AbstractIn 1953, Linnik introduced the probability density pα(x) defined in terms of its characteris...
International audienceIn this paper we study the distribution of pairs (d1, d2) of positive integers...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
AbstractIn 1953, Linnik introduced the probability density pα(x) defined by means of its characteris...
Abstract. In this paper, we investigate linear relations among the Eu-ler function of nearby integer...
Closed forms are derived for the probability density function (PDF) of the stable distribution S α (...
AbstractLet N denote the set of positive integers. The asymptotic density of the set A⊆N is d(A)=lim...
91 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981.Let (phi)(n) denote Euler's fu...
In this work we will consider several questions concerning the asymptotic nature of arithmetic funct...
AbstractLet ps(n) = n−sζ(s) for n = 1,2,3,… and s > 1 be used to define a probability distribution P...
AbstractLet d(ω; α, γ) be the number of divisors of the Gaussian integer ω which lie in the arithmet...
AbstractLet σα(n) be the sum of the αth power of the positive divisors of n. We establish an asympto...
AbstractLet {ϵd} be a sequence of nonnegative numbers and f(n) = Σ ϵd, the sum being over divisors d...
Let σ(n)=∑d∣nd be the usual sum-of-divisors function. In 1933, Davenport showed that n/σ(n) possesse...
Plünnecke proved that if B ⊆ N is a basis of order h> 1, i.e., σ(hB) = 1, then σ(A+B)> σ(A)1 ...
AbstractIn 1953, Linnik introduced the probability density pα(x) defined in terms of its characteris...
International audienceIn this paper we study the distribution of pairs (d1, d2) of positive integers...
International audienceLet b ≥ 2 be an integer and let s b (n) denote the sum of the digits of the re...
AbstractIn 1953, Linnik introduced the probability density pα(x) defined by means of its characteris...
Abstract. In this paper, we investigate linear relations among the Eu-ler function of nearby integer...
Closed forms are derived for the probability density function (PDF) of the stable distribution S α (...
AbstractLet N denote the set of positive integers. The asymptotic density of the set A⊆N is d(A)=lim...
91 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981.Let (phi)(n) denote Euler's fu...
In this work we will consider several questions concerning the asymptotic nature of arithmetic funct...
AbstractLet ps(n) = n−sζ(s) for n = 1,2,3,… and s > 1 be used to define a probability distribution P...
AbstractLet d(ω; α, γ) be the number of divisors of the Gaussian integer ω which lie in the arithmet...
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